The goal of this project is to develop improved statistical methods for the analysis of data from human studies. In disease screening studies, it is difficult to obtain direct information on the age at onset of disease, the timing of past exposures, and the rate of disease progression. Work has progressed in the development of methods for disease screening studies, motivated by the NIEHS uterine fibroid (leiomyoma) study conducted by Donna Baird. We developed a Bayesian approach that incorporates current disease severity information in estimating incidence and rates of disease progression. Based on this approach, we found African American woman to have not only higher incidence rates but also higher rates of progression of leiomyoma. We also developed a general model for assessing beneficial effects of time-dependent covariates on delaying disease onset and curing preexisting disease. This model was motivated by tumor biology, and was applied to assess the effects of childbirth on uterine leiomyoma. The results provided motivation for a follow-up study of the impact of pregnancy on fibroids. In addition to methodology motivated by screening studies, we have developed general procedures for incorporating order constraints into regression models and for assessing sources of heterogeneity in the setting of generalized linear mixed models. These methods have general applications in epidemiology and toxicology studies.